Problem: Vanessa is 2 times as old as Kevin. 21 years ago, Vanessa was 9 times as old as Kevin. How old is Kevin now?
Explanation: We can use the given information to write down two equations that describe the ages of Vanessa and Kevin. Let Vanessa's current age be $v$ and Kevin's current age be $k$ The information in the first sentence can be expressed in the following equation: $v = 2k$ 21 years ago, Vanessa was $v - 21$ years old, and Kevin was $k - 21$ years old. The information in the second sentence can be expressed in the following equation: $v - 21 = 9(k - 21)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to use our first equation for $v$ and substitute it into our second equation. Our first equation is: $v = 2k$ . Substituting this into our second equation, we get: $2k$ $-$ $21 = 9(k - 21)$ which combines the information about $k$ from both of our original equations. Simplifying the right side of this equation, we get: $2 k - 21 = 9 k - 189$ Solving for $k$ , we get: $7 k = 168.$ $k = 24$.